Question

Two parallel plate capacitors, each of capacitance 40 µF, are connected in series. The space between the plates of one capacitor is filled with a material of dielectric constant K = 4. The equivalent capacitance of the system would be:

• A. 30 µF
• B. 31 µF
• C. 32 µF
• D. 33 µF

Answer 1

The Correct Option is C

Capacitor System Solution:

Given:

• Two capacitors, each with an initial capacitance of 40 μF, are connected in series.
• One of the capacitors has a dielectric material with a dielectric constant (K) of 4.

Calculations:

1. The capacitance of the capacitor with the dielectric inserted is calculated as \( C_1 = K \times C = 4 \times 40\mu F = 160\mu F \).

2. The capacitance of the second capacitor remains \( C_2 = 40\mu F \).

3. The formula for equivalent capacitance in series is applied:

\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} = \frac{1}{160} + \frac{1}{40} = \frac{1}{32} \]

4. The resulting equivalent capacitance is \( C_{eq} = 32\mu F \).

Correct Answer: \(32\  μF\)